Coordination of distributed/parallel multiple-grid domain decomposition

Abstract

A w orkable approach for the solution of many (numerical and non-numerical) problems is domain decomposition. If a problem can be divided into a number of sub-problems that can be solved in a distributed/parallel fashion, the overall performance can signi cantly improve. In this paper, we discuss one of our experiments using the new coordination language MANIFOLD to solve an instance of the classical optimization problem by domain decomposition. We demonstrate the applicability o f MANIFOLD in expressing the solutions to domain decomposition problems in a generic way and its utility i n p roducing executable code that can carry out such solutions in both distributed and parallel environments.The multiple-grid domain decomposition method used in this paper is based on adaptive partitioning of the domain and results in highly irregular grids as shown in the examples. The implementation of the distributed/parallel approach presented in this paper looks very promising and its coordinator modules are generally applicable.

Reusable coordinator modules for massively concurrent applications

“…Extension of this example for multiple-grid domain decomposition is straightforward and involves only a small change to the main program of this application. 26 We need four simple computation modules for our current example: ap printobjects, Split, AtomicEval and AtomicObjMerger. An instance of ap printobjects simply prints the units it reads from its input, each of which describes a (sub-)domain and the x,y and z values for the estimated maximum z value in that (sub-)domain.…”

“…Indeed, we have a small computational steering environment built around this example, using Manifold coordinators and a few generic graphics interaction modules. 26 The user interface for this program graphically shows the ongoing activity of various atomic evaluators (that may be running on different hosts) and allows the user to interactively direct the focus of the attention of the program onto one or more areas of interest, simply by drawing a box to designate a sub-domain. Figure 5 shows a snap-shot of a simple visualizer interface as our 2 × 2 distributed domain decomposition optimization application moved on (in its fifth iteration) to the top-right corner sub-domain in the run that produced the above output.…”

Coordination languages for parallel programming

“…The computation modules, on the other hand, cannot possibly change the topology of this graph, making both sets of modules easier to verify and more reusable. The concept of reusable pure coordination modules in MANIFOLD is demonstrated, e.g., by using (the object code of) the same MANI-FOLD coordinator program that was developed for a parallel/ distributed bucket sort algorithm, to perform function evaluation and numerical optimization using domain decomposition [25,26].…”

“…Analogous to Fork, an instance of Philosopher enters an infinite loop upon its activation (lines [26][27][28][29][30][31][32][33][34][35]. In each iteration of this loop, a Philosopher instance first does its thinking Cline 27), then waits to obtain a dining ticket (line 28), and finally, declares its intention to eat by raising the events request and its private ready, and goes into a wait state.…”

Reusable coordinator modules for massively concurrent applications

“…Extension of this example for multiple-grid domain decomposition is straightforward and involves only a small change to the main program of this application. 26 We need four simple computation modules for our current example: ap printobjects, Split, Atom-icEval and AtomicObjMerger. An instance of ap printobjects simply prints the units it reads from its input, each of which describes a (sub-)domain and the x,y and z values for the estimated maximum z value in that (sub-)domain.…”